
In Any Way but This. Pattern Avoidance. The Basics. 167
Our plan is to bring Lemmas 4.34 and 4.36 together to prove Theorem 4.32.
This needs some preparation. Optimally, we would take a 1342-avoiding inde-
composable n-permutation p, associate its entries to the nodes of an unlabeled
plane tree T , then define the labels of this tree so that it becomes a β(0, 1)-
tree. The question is, however, how do we know what T we should use, and
if T is given, how do we know in what order we should write the entries of
p to the nodes of T . In what follows, we develop the notions to decide these
questions.
DEFINITION 4.38 Two n-permutations x and y are said to